OTC 2L 10s

Omnitetrachordal MODMOS scales
2L+10s

This OTC scale pattern has two classes (with different tetrachordal divisions). Only a few other scales of the form 2L+ns are known to have this property.

temperaments: injera ?

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Class 1

12 tones (5+2+5)

Dual of OTC 10L+2s. Probably only useful for small values of L/s.

P = 0.8849491924
Q = 3.8274237885 (4/3 = L+3.5s)

L = 100.00 to 600.00 cents (260.15 cents @ Q)
s = 0.00 to 100.00 cents (67.97 cents @ Q)

9/8 = 2s (0.00 to 200.00 cents)
4/3 = L+4s (500.00 to 600.00 cents)
MOS generator = s (0.00 to 100.00 cents)
MOS period = 1/2 octave (600.00 cents)

notable EDOs: 14, 16, 26, 38

LsssssLsssss (MOS, not OTC)
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LssssLssssss (OTC MODMOS) - gen chains 7,5

symmetric modes:
sssLssssLsss
ssLssssssLss

all modes:

	ssLss ss ssLss
	sLsss ss sLsss
	Lssss ss Lssss
ss ssssL ssssL
ss sssLs sssLs
ss ssLss ssLss		ssssL ssssL ss
ss sLsss sLsss		sssLs sssLs ss
ss Lssss Lssss		ssLss ssLss ss
		sLsss sLsss ss
		Lssss Lssss ss
	ssssL ss ssssL
	sssLs ss sssLs

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Class 2

12 tones (4+4+4)

Only works at high values of L/s.

Q2 = 3.8274237885 (4/3 = L+3.5s)
P = 6.7698983847
Q1 = 9.7123729809 (4/3 = L+2.5s)

L = 100.00 to 600.00 cents (260.15 cents @ Q2, 345.11 cents @ P, 396.09 cents @ Q1)
s = 0.00 to 100.00 cents (67.97 cents @ Q2, 50.98 cents @ P, 40.78 cents @ Q1)

9/8 = 4s (0.00 to 400.00 cents)
4/3 = L+3s (400.00 to 600.00 cents)
MOS generator = s (0.00 to 100.00 cents)
MOS period = 1/2 octave (600.00 cents)

notable EDOs: 20, 22, 24

LsssssLsssss (MOS, not OTC)
    | |     
LsssLsssssss (OTC MODMOS) - gen chains 8,4

all modes:

		Lsss Lsss ssss
	sssL ssss sssL
	ssLs ssss ssLs
	sLss ssss sLss
	Lsss ssss Lsss
ssss sssL sssL
ssss ssLs ssLs
ssss sLss sLss
ssss Lsss Lsss
		sssL sssL ssss
		ssLs ssLs ssss
		sLss sLss ssss

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See also

• Omnitetrachordality
• Gallery of omnitetrachordal scales